Why do you think America avoided war with Great Britain but not Mexico?

Answer 1

They didn't - ever hear of "the War of 1812"? That was fought between the USA and Great Britain from 1812 to 1814. The Mexican-American war was only 32 years later - from 1846 to 1848. Some soldiers served in both wars; for example President Zachary Taylor commanded the defending US forces in the Battle of Fort Harrison during the War of 1812 and was the commanding General of US forces during the Mexican-American war (after Gen. Winfield Scott was removed due to conflicts with Pres. Polk)

Possibly the question was intended to refer to the potential conflict between the US and Great Britain over the Oregon at roughly the same time that trouble was brewing with Mexico following the annexation of Texas. The British were very interested in negotiating a resolution of the boundary dispute in the Oregon region (and avoiding war).

US President Polk found it much easier to negotiate with Great Britain and avoid war than to get Mexico to negotiate, convince immigrants from the USA into California, New Mexico, and Texas areas to quit fighting with Mexico, or convince Congress not to follow up with "Manifest Destiny" and expand into those areas (in fact he was in favor of the expansion - after all, he sent John Slidell to Mexico City to try to negotiate for the purchase of all that territory).

The vast majority of Mexicans felt retaining ALL of their territory (including the areas of California, New Mexico, and the area between the Rio Grande and Nueces River, which the U.S. attempted to purchase prior to the conflict) was a matter of honor. They were insulted by the U.S. offers and had no interest in negotiations. Another reason negotiations with Mexico were impossible is that the political situation in Mexico was in chaos - with no one really having enough power to negotiate without being pushed out of power by the other competing Mexican political factions. In 1846 alone (the year the war started), the presidency changed hands four times, the war ministry six times, and the finance ministry sixteen times.